Title:
Symmetry and localization for magnetic Schroedinger operators: Landau levels, Gabor frames and all that

Abstract: We investigate the relation between broken time-reversal symmetry and
localization of the electronic states, in the explicitly tractable case of the
Landau model. We first review, for the reader's convenience, the symmetries of
the Landau Hamiltonian and the relation of the latter with the Segal-Bargmann
representation of Quantum Mechanics. We then study the localization properties
of the Landau eigenstates by applying an abstract version of the Balian-Low
Theorem to the operators corresponding to the coordinates of the centre of the
cyclotron orbit in the classical theory. Our proof of the Balian-Low Theorem,
although based on Battle's main argument, has the advantage of being
representation-independent.

Comments:

18 pages, no figures. Version 2 : Final version, to appear in Acta Applicandae Mathematicae